62nd Ukrainian National Mathematical Olympiad, Third Round, First Tour

Question

What smallest value can be attained by the expression (x + y + |x - y|)^2xy for positive x, y?

Accepted Answer

We assume x y, then we can rewrite as: (x + y + |x - y|)^2xy = (x + y + x - y)^2xy = (2x)^2xy = 4x^2xy = 4xy 4 When x = y, we get equality.